R Notebook

Run download_data.Rmd and percentage_of_regional_richness.Rmd First!

library(randomForest)

randomForest 4.6-14
Type rfNews() to see new features/changes/bug fixes.

library(reshape2)
library(rpart)
library(ggplot2)

Attaching package: ‘ggplot2’

The following object is masked from ‘package:randomForest’:

    margin

library(tidyverse)

Registered S3 methods overwritten by 'dbplyr':
  method         from
  print.tbl_lazy     
  print.tbl_sql      
── Attaching packages ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── tidyverse 1.3.1 ──
✓ tibble  3.1.2     ✓ dplyr   1.0.7
✓ tidyr   1.1.3     ✓ stringr 1.4.0
✓ readr   1.4.0     ✓ forcats 0.5.1
✓ purrr   0.3.4     
── Conflicts ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
x dplyr::combine()  masks randomForest::combine()
x dplyr::filter()   masks stats::filter()
x dplyr::lag()      masks stats::lag()
x ggplot2::margin() masks randomForest::margin()

library(multcomp)

Loading required package: mvtnorm
Loading required package: survival
Loading required package: TH.data
Loading required package: MASS

Attaching package: ‘MASS’

The following object is masked from ‘package:dplyr’:

    select


Attaching package: ‘TH.data’

The following object is masked from ‘package:MASS’:

    geyser

library(car)

Loading required package: carData
Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     
Registered S3 methods overwritten by 'car':
  method                          from
  influence.merMod                lme4
  cooks.distance.influence.merMod lme4
  dfbeta.influence.merMod         lme4
  dfbetas.influence.merMod        lme4

Attaching package: ‘car’

The following object is masked from ‘package:dplyr’:

    recode

The following object is masked from ‘package:purrr’:

    some

city_data

length(city_data$city_gdp_per_population[!is.na(city_data$city_gdp_per_population)])

[1] 30

length(city_data$percentage_urban_area_as_open_public_spaces[!is.na(city_data$percentage_urban_area_as_open_public_spaces)])

[1] 61

length(city_data$happiness_future_life[!is.na(city_data$happiness_future_life)])

[1] 65

length(city_data$mean_population_exposure_to_pm2_5_2019[!is.na(city_data$mean_population_exposure_to_pm2_5_2019)])

[1] 131

fetch_city_data_for <- function(pool_name, include_city_name = F) {
  results_filename <- paste(paste('percentage_of_regional_richness__output_', pool_name, 'city', 'richness', 'intercept', sep = "_"), "csv", sep = ".")
  results <- read_csv(results_filename)
  
  joined <- left_join(city_data, results)
  
  required_columns <- c("population_growth", "rainfall_monthly_min", "rainfall_annual_average", "rainfall_monthly_max", "temperature_annual_average", "temperature_monthly_min", "temperature_monthly_max", "happiness_negative_effect", "happiness_positive_effect", "happiness_future_life", "number_of_biomes", "realm", "biome_name", "region_20km_includes_estuary", "region_50km_includes_estuary", "region_100km_includes_estuary", "city_includes_estuary", "region_20km_average_pop_density", "region_50km_average_pop_density", "region_100km_average_pop_density", "city_max_pop_density", "city_average_pop_density", "mean_population_exposure_to_pm2_5_2019", "region_20km_cultivated", "region_20km_urban", "region_50km_cultivated", "region_50km_urban", "region_100km_cultivated", "region_100km_urban", "region_20km_elevation_delta", "region_20km_mean_elevation", "region_50km_elevation_delta", "region_50km_mean_elevation", "region_100km_elevation_delta", "region_100km_mean_elevation", "city_elevation_delta", "city_mean_elevation", "urban", "shrubs", "permanent_water", "open_forest", "herbaceous_wetland", "herbaceous_vegetation", "cultivated", "closed_forest", "share_of_population_within_400m_of_open_space", "percentage_urban_area_as_streets", "percentage_urban_area_as_open_public_spaces_and_streets", "percentage_urban_area_as_open_public_spaces", "city_gdp_per_population", "city_ndvi", "city_ssm", "city_susm", "region_20km_ndvi", "region_20km_ssm", "region_20km_susm", "region_50km_ndvi", "region_50km_ssm", "region_50km_susm", "region_100km_ndvi", "region_100km_ssm", "region_100km_susm", "city_percentage_protected", "region_20km_percentage_protected", "region_50km_percentage_protected", "region_100km_percentage_protected")
  
  if (include_city_name) {
    required_columns <- append(c("name"), required_columns)
  }
  
  required_columns <- append(c("response"), required_columns)
  
  joined[,required_columns]
}

merlin_city_data <- fetch_city_data_for('merlin')

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)

Joining, by = "name"

merlin_city_data

merlin_city_data_fixed <- rfImpute(response ~ ., merlin_city_data)

     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    21.14   117.27 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    21.15   117.32 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    21.42   118.82 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    21.36   118.50 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    21.47   119.09 |

merlin_city_data_fixed

ggplot(merlin_city_data_fixed, aes(response)) + geom_histogram(binwidth = 2)

source('./helper__random_forest_selection_functions.R')

scale_parameter_name <- function(scale, postscript) {
  paste('region', paste(scale, 'km', sep = ''), postscript, sep = '_')  
}

scale_parameters <- function(postscript) {
  c(scale_parameter_name(20, postscript), scale_parameter_name(50, postscript), scale_parameter_name(100, postscript))
}

scales_parameters_without <- function(scale_to_exclude, postscript) {
  scales <- scale_parameters(postscript)
  scales[scales != scale_parameter_name(scale_to_exclude, postscript)]
}

select_scales <- function(urban, cultivated, elevation_delta, mean_elevation, average_pop_density, includes_estuary, ssm, susm, ndvi, percentage_protected) {
  append(
    append(
      append(
        append(
          scales_parameters_without(scale_to_exclude = urban, postscript = 'urban'),
          scales_parameters_without(scale_to_exclude = cultivated, postscript = 'cultivated')
        ),
        append(
          scales_parameters_without(scale_to_exclude = elevation_delta, postscript = 'elevation_delta'),
          scales_parameters_without(scale_to_exclude = mean_elevation, postscript = 'mean_elevation')
        )
      ),
      append(
        append(
          scales_parameters_without(scale_to_exclude = average_pop_density, postscript = 'average_pop_density'),
          scales_parameters_without(scale_to_exclude = includes_estuary, postscript = 'includes_estuary')
        ),
        append(
          scales_parameters_without(scale_to_exclude = ssm, postscript = 'ssm'),
          scales_parameters_without(scale_to_exclude = susm, postscript = 'susm')
        )
      )
    ),
    append(
      scales_parameters_without(scale_to_exclude = ndvi, postscript = 'ndvi'),
      scales_parameters_without(scale_to_exclude = percentage_protected, postscript = 'percentage_protected')
    )
  )
}

select_scales(urban = 20, cultivated = 100, elevation_delta = 20, mean_elevation = 100, average_pop_density = NA, includes_estuary = NA, ssm = 20, susm = 20, ndvi = 100, percentage_protected = NA)

 [1] "region_50km_urban"                 "region_100km_urban"                "region_20km_cultivated"            "region_50km_cultivated"            "region_50km_elevation_delta"      
 [6] "region_100km_elevation_delta"      "region_20km_mean_elevation"        "region_50km_mean_elevation"        "region_20km_average_pop_density"   "region_50km_average_pop_density"  
[11] "region_100km_average_pop_density"  "region_20km_includes_estuary"      "region_50km_includes_estuary"      "region_100km_includes_estuary"     "region_50km_ssm"                  
[16] "region_100km_ssm"                  "region_50km_susm"                  "region_100km_susm"                 "region_20km_ndvi"                  "region_50km_ndvi"                 
[21] "region_20km_percentage_protected"  "region_50km_percentage_protected"  "region_100km_percentage_protected"

select_scales(urban = , cultivated = , elevation_delta = , mean_elevation = , average_pop_density = , includes_estuary = , ssm = , susm = , ndvi =, percentage_protected = )

select_variables_from_random_forest(merlin_city_data_fixed)

 [1] "region_50km_ssm"                                         "biome_name"                                              "region_100km_ssm"                                       
 [4] "region_50km_elevation_delta"                             "region_20km_elevation_delta"                             "permanent_water"                                        
 [7] "region_20km_ssm"                                         "region_20km_urban"                                       "region_100km_elevation_delta"                           
[10] "shrubs"                                                  "city_ndvi"                                               "city_gdp_per_population"                                
[13] "region_50km_urban"                                       "region_20km_cultivated"                                  "temperature_annual_average"                             
[16] "region_50km_cultivated"                                  "region_100km_cultivated"                                 "temperature_monthly_min"                                
[19] "region_100km_susm"                                       "herbaceous_wetland"                                      "region_50km_average_pop_density"                        
[22] "region_50km_ndvi"                                        "city_max_pop_density"                                    "region_100km_average_pop_density"                       
[25] "temperature_monthly_max"                                 "happiness_positive_effect"                               "region_100km_urban"                                     
[28] "realm"                                                   "city_average_pop_density"                                "region_20km_average_pop_density"                        
[31] "region_50km_percentage_protected"                        "region_100km_percentage_protected"                       "city_ssm"                                               
[34] "city_elevation_delta"                                    "city_mean_elevation"                                     "region_50km_susm"                                       
[37] "region_20km_mean_elevation"                              "region_20km_percentage_protected"                        "herbaceous_vegetation"                                  
[40] "urban"                                                   "rainfall_monthly_max"                                    "city_percentage_protected"                              
[43] "cultivated"                                              "region_100km_mean_elevation"                             "region_20km_susm"                                       
[46] "city_susm"                                               "rainfall_annual_average"                                 "population_growth"                                      
[49] "happiness_negative_effect"                               "rainfall_monthly_min"                                    "share_of_population_within_400m_of_open_space"          
[52] "region_100km_ndvi"                                       "region_50km_mean_elevation"                              "percentage_urban_area_as_open_public_spaces_and_streets"
[55] "open_forest"                                             "region_20km_ndvi"                                        "percentage_urban_area_as_streets"                       
[58] "closed_forest"                                           "percentage_urban_area_as_open_public_spaces"            

select_variables_from_random_forest(merlin_city_data_fixed_single_scale)

 [1] "region_50km_ssm"                                         "region_50km_elevation_delta"                             "biome_name"                                             
 [4] "city_gdp_per_population"                                 "permanent_water"                                         "city_ndvi"                                              
 [7] "temperature_annual_average"                              "region_20km_cultivated"                                  "shrubs"                                                 
[10] "temperature_monthly_min"                                 "region_20km_urban"                                       "herbaceous_wetland"                                     
[13] "city_max_pop_density"                                    "city_ssm"                                                "region_50km_average_pop_density"                        
[16] "city_average_pop_density"                                "realm"                                                   "temperature_monthly_max"                                
[19] "happiness_positive_effect"                               "region_50km_percentage_protected"                        "rainfall_monthly_max"                                   
[22] "city_mean_elevation"                                     "region_100km_susm"                                       "city_percentage_protected"                              
[25] "cultivated"                                              "happiness_future_life"                                   "rainfall_annual_average"                                
[28] "urban"                                                   "happiness_negative_effect"                               "region_20km_mean_elevation"                             
[31] "share_of_population_within_400m_of_open_space"           "rainfall_monthly_min"                                    "population_growth"                                      
[34] "region_50km_ndvi"                                        "open_forest"                                             "percentage_urban_area_as_open_public_spaces_and_streets"
[37] "percentage_urban_area_as_open_public_spaces"             "closed_forest"                                           "percentage_urban_area_as_streets"                       
[40] "city_susm"                                              

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm")])

[1] "Mean  25.1327179439473 , SD:  0.216956545963824 , Mean + SD:  25.3496744899111"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta")])

[1] "Mean  19.6242084196811 , SD:  0.282975547429027 , Mean + SD:  19.9071839671101"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name")])

[1] "Mean  19.2510597598754 , SD:  0.237378636197946 , Mean + SD:  19.4884383960734"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population")])

[1] "Mean  17.5667371783479 , SD:  0.225378699860072 , Mean + SD:  17.792115878208"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water")])

[1] "Mean  17.764917887126 , SD:  0.253600901946159 , Mean + SD:  18.0185187890721"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi")])

[1] "Mean  18.1713060031583 , SD:  0.274695354565878 , Mean + SD:  18.4460013577242"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average")])

[1] "Mean  18.4997318566786 , SD:  0.236978359007798 , Mean + SD:  18.7367102156864"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average",  "region_20km_cultivated")])

[1] "Mean  18.151366275243 , SD:  0.310327391925745 , Mean + SD:  18.4616936671687"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average",  "region_20km_cultivated", "shrubs")])

[1] "Mean  18.1996679903146 , SD:  0.32269285565908 , Mean + SD:  18.5223608459736"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average",  "region_20km_cultivated", "shrubs", "temperature_monthly_min")])

[1] "Mean  18.3993943899942 , SD:  0.305819135869039 , Mean + SD:  18.7052135258632"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average",  "region_20km_cultivated", "shrubs", "temperature_monthly_min", "region_20km_urban")])

[1] "Mean  18.2983031433913 , SD:  0.27248663139474 , Mean + SD:  18.570789774786"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average",  "region_20km_cultivated", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland")])

[1] "Mean  18.4617430190922 , SD:  0.256208381412962 , Mean + SD:  18.7179514005052"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average",  "region_20km_cultivated", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density")])

[1] "Mean  18.3158359875326 , SD:  0.270120208103265 , Mean + SD:  18.5859561956359"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average",  "region_20km_cultivated", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_ssm")])

[1] "Mean  18.6428753216302 , SD:  0.26630095939741 , Mean + SD:  18.9091762810276"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average",  "region_20km_cultivated", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_ssm", "region_50km_average_pop_density")])

[1] "Mean  18.8052699642646 , SD:  0.246919293071592 , Mean + SD:  19.0521892573362"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average",  "region_20km_cultivated", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_ssm", "region_50km_average_pop_density", "city_average_pop_density")])

[1] "Mean  19.0500779913321 , SD:  0.281562617871374 , Mean + SD:  19.3316406092035"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average",  "region_20km_cultivated", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_ssm", "region_50km_average_pop_density", "city_average_pop_density", "realm")])

[1] "Mean  18.9638490604482 , SD:  0.304880439343029 , Mean + SD:  19.2687294997913"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average",  "region_20km_cultivated", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_ssm", "region_50km_average_pop_density", "city_average_pop_density", "realm", "temperature_monthly_max")])

[1] "Mean  19.1737445329045 , SD:  0.30237720581189 , Mean + SD:  19.4761217387164"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average",  "region_20km_cultivated", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_ssm", "region_50km_average_pop_density", "city_average_pop_density", "realm", "temperature_monthly_max", "happiness_positive_effect")])

[1] "Mean  19.2237641823427 , SD:  0.305017487786321 , Mean + SD:  19.5287816701291"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average",  "region_20km_cultivated", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_ssm", "region_50km_average_pop_density", "city_average_pop_density", "realm", "temperature_monthly_max", "happiness_positive_effect", "region_50km_percentage_protected")])

[1] "Mean  19.2731318874597 , SD:  0.293953451788727 , Mean + SD:  19.5670853392485"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "biome_name", "city_gdp_per_population", "permanent_water", "city_ndvi", "temperature_annual_average",  "region_20km_cultivated", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_ssm", "region_50km_average_pop_density", "city_average_pop_density", "realm", "temperature_monthly_max", "happiness_positive_effect", "region_50km_percentage_protected", "rainfall_monthly_max")])

[1] "Mean  19.3829197721043 , SD:  0.293734015304046 , Mean + SD:  19.6766537874083"

“region_50km_ssm”, “region_50km_elevation_delta”, “biome_name”, “city_gdp_per_population”

birdlife_city_data <- fetch_city_data_for('birdlife')

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)

Joining, by = "name"

birdlife_city_data

birdlife_city_data_fixed <- rfImpute(response ~ ., birdlife_city_data)

     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.641    89.30 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.686    90.01 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |     5.74    90.87 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.665    89.67 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.797    91.77 |

birdlife_city_data_fixed

select_variables_from_random_forest(birdlife_city_data_fixed)

 [1] "population_growth"                                       "region_50km_ssm"                                         "region_100km_ssm"                                       
 [4] "city_ndvi"                                               "region_100km_cultivated"                                 "region_50km_cultivated"                                 
 [7] "region_20km_ssm"                                         "region_100km_susm"                                       "region_20km_susm"                                       
[10] "rainfall_monthly_max"                                    "biome_name"                                              "permanent_water"                                        
[13] "temperature_monthly_min"                                 "region_50km_susm"                                        "region_20km_average_pop_density"                        
[16] "rainfall_monthly_min"                                    "city_ssm"                                                "region_50km_ndvi"                                       
[19] "region_100km_ndvi"                                       "region_20km_ndvi"                                        "percentage_urban_area_as_open_public_spaces_and_streets"
[22] "share_of_population_within_400m_of_open_space"           "region_50km_average_pop_density"                         "percentage_urban_area_as_open_public_spaces"            
[25] "mean_population_exposure_to_pm2_5_2019"                  "region_20km_cultivated"                                  "city_average_pop_density"                               
[28] "region_100km_average_pop_density"                        "region_100km_urban"                                      "temperature_annual_average"                             
[31] "region_20km_elevation_delta"                             "percentage_urban_area_as_streets"                        "rainfall_annual_average"                                
[34] "city_susm"                                               "realm"                                                   "region_50km_elevation_delta"                            
[37] "shrubs"                                                  "region_20km_urban"                                       "happiness_future_life"                                  
[40] "region_100km_percentage_protected"                       "city_max_pop_density"                                    "city_elevation_delta"                                   
[43] "region_100km_mean_elevation"                             "happiness_positive_effect"                               "region_20km_percentage_protected"                       
[46] "region_50km_urban"                                       "region_50km_percentage_protected"                        "region_50km_mean_elevation"                             
[49] "city_mean_elevation"                                     "closed_forest"                                           "herbaceous_wetland"                                     
[52] "city_gdp_per_population"                                 "urban"                                                   "region_20km_mean_elevation"                             
[55] "region_100km_elevation_delta"                            "open_forest"                                             "herbaceous_vegetation"                                  
[58] "city_percentage_protected"                               "cultivated"                                              "happiness_negative_effect"                              
[61] "temperature_monthly_max"                                

select_variables_from_random_forest(birdlife_city_data_fixed_single_scale)

 [1] "population_growth"                                       "region_50km_ssm"                                         "region_100km_cultivated"                                
 [4] "city_ndvi"                                               "biome_name"                                              "region_100km_susm"                                      
 [7] "rainfall_monthly_min"                                    "rainfall_monthly_max"                                    "city_ssm"                                               
[10] "region_20km_average_pop_density"                         "permanent_water"                                         "temperature_monthly_min"                                
[13] "percentage_urban_area_as_open_public_spaces_and_streets" "region_50km_ndvi"                                        "temperature_annual_average"                             
[16] "region_100km_urban"                                      "region_20km_elevation_delta"                             "rainfall_annual_average"                                
[19] "share_of_population_within_400m_of_open_space"           "percentage_urban_area_as_open_public_spaces"             "mean_population_exposure_to_pm2_5_2019"                 
[22] "city_average_pop_density"                                "shrubs"                                                  "city_susm"                                              
[25] "realm"                                                   "percentage_urban_area_as_streets"                        "city_max_pop_density"                                   
[28] "city_elevation_delta"                                    "city_gdp_per_population"                                 "happiness_future_life"                                  
[31] "open_forest"                                             "happiness_positive_effect"                               "closed_forest"                                          
[34] "urban"                                                   "city_mean_elevation"                                     "cultivated"                                             
[37] "temperature_monthly_max"                                 "herbaceous_vegetation"                                   "happiness_negative_effect"                              

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth")])

[1] "Mean  6.35021321550458 , SD:  0.0593939328578979 , Mean + SD:  6.40960714836247"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm")])

[1] "Mean  4.84915699583042 , SD:  0.0818098257429198 , Mean + SD:  4.93096682157334"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated")])

[1] "Mean  5.28049378048091 , SD:  0.0775169354173377 , Mean + SD:  5.35801071589825"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi")])

[1] "Mean  5.12061471889155 , SD:  0.0874280154413976 , Mean + SD:  5.20804273433295"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name")])

[1] "Mean  5.15325796547024 , SD:  0.0694110168148363 , Mean + SD:  5.22266898228508"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi")])

[1] "Mean  5.2434172819644 , SD:  0.0806361112621407 , Mean + SD:  5.32405339322654"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density")])

[1] "Mean  5.24489256584117 , SD:  0.0766441089091058 , Mean + SD:  5.32153667475027"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density", "permanent_water")])

[1] "Mean  5.04554202135548 , SD:  0.0836282380010259 , Mean + SD:  5.12917025935651"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density", "permanent_water", "temperature_monthly_min")])

[1] "Mean  5.12412938740328 , SD:  0.0730235792725426 , Mean + SD:  5.19715296667582"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density", "permanent_water", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces_and_streets")])

[1] "Mean  5.13911115863577 , SD:  0.0955009377977672 , Mean + SD:  5.23461209643353"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density", "permanent_water", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces_and_streets", "region_50km_ndvi")])

[1] "Mean  5.13817856130947 , SD:  0.0716785842473469 , Mean + SD:  5.20985714555681"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density", "permanent_water", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces_and_streets", "region_50km_ndvi", "temperature_annual_average")])

[1] "Mean  5.215868046915 , SD:  0.0765190804551457 , Mean + SD:  5.29238712737014"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density", "permanent_water", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces_and_streets", "region_50km_ndvi", "temperature_annual_average", "region_100km_urban")])

[1] "Mean  5.1564082999918 , SD:  0.0829912635065974 , Mean + SD:  5.2393995634984"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density", "permanent_water", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces_and_streets", "region_50km_ndvi", "temperature_annual_average", "region_100km_urban", "region_20km_elevation_delta")])

[1] "Mean  5.14814218492991 , SD:  0.0749108151793109 , Mean + SD:  5.22305300010922"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density", "permanent_water", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces_and_streets", "region_50km_ndvi", "temperature_annual_average", "region_100km_urban", "region_20km_elevation_delta", "rainfall_annual_average")])

[1] "Mean  5.23244059006495 , SD:  0.0774719747962131 , Mean + SD:  5.30991256486116"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density", "permanent_water", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces_and_streets", "region_50km_ndvi", "temperature_annual_average", "region_100km_urban", "region_20km_elevation_delta", "rainfall_annual_average", "share_of_population_within_400m_of_open_space")])

[1] "Mean  5.23874499037273 , SD:  0.0863811628674503 , Mean + SD:  5.32512615324018"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density", "permanent_water", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces_and_streets", "region_50km_ndvi", "temperature_annual_average", "region_100km_urban", "region_20km_elevation_delta", "rainfall_annual_average", "share_of_population_within_400m_of_open_space", "percentage_urban_area_as_open_public_spaces")])

[1] "Mean  5.35567550025148 , SD:  0.0933112444550703 , Mean + SD:  5.44898674470655"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density", "permanent_water", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces_and_streets", "region_50km_ndvi", "temperature_annual_average", "region_100km_urban", "region_20km_elevation_delta", "rainfall_annual_average", "share_of_population_within_400m_of_open_space", "percentage_urban_area_as_open_public_spaces", "mean_population_exposure_to_pm2_5_2019")])

[1] "Mean  5.36212621452981 , SD:  0.0841422083666618 , Mean + SD:  5.44626842289647"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density", "permanent_water", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces_and_streets", "region_50km_ndvi", "temperature_annual_average", "region_100km_urban", "region_20km_elevation_delta", "rainfall_annual_average", "share_of_population_within_400m_of_open_space", "percentage_urban_area_as_open_public_spaces", "mean_population_exposure_to_pm2_5_2019", "city_average_pop_density")])

[1] "Mean  5.38148077142908 , SD:  0.0792499982773259 , Mean + SD:  5.46073076970641"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density", "permanent_water", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces_and_streets", "region_50km_ndvi", "temperature_annual_average", "region_100km_urban", "region_20km_elevation_delta", "rainfall_annual_average", "share_of_population_within_400m_of_open_space", "percentage_urban_area_as_open_public_spaces", "mean_population_exposure_to_pm2_5_2019", "city_average_pop_density", "shrubs")])

[1] "Mean  5.37060887208482 , SD:  0.100105116953198 , Mean + SD:  5.47071398903801"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "region_100km_cultivated", "city_ndvi", "biome_name", "city_ndvi", "region_20km_average_pop_density", "permanent_water", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces_and_streets", "region_50km_ndvi", "temperature_annual_average", "region_100km_urban", "region_20km_elevation_delta", "rainfall_annual_average", "share_of_population_within_400m_of_open_space", "percentage_urban_area_as_open_public_spaces", "mean_population_exposure_to_pm2_5_2019", "city_average_pop_density", "shrubs", "city_susm")])

[1] "Mean  5.47535632462927 , SD:  0.0825514964435405 , Mean + SD:  5.55790782107281"

“population_growth”, “region_50km_ssm”

So….
Merlin: “region_50km_ssm”, “region_50km_elevation_delta”, “biome_name”, “city_gdp_per_population” Birdlife: “population_growth”, “region_50km_ssm”

Try Modelling

library(boot)

Attaching package: ‘boot’

The following object is masked from ‘package:car’:

    logit

The following object is masked from ‘package:survival’:

    aml

merlin_city_data_named <- fetch_city_data_for('merlin', T)

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)

Joining, by = "name"

birdlife_city_data_named <- fetch_city_data_for('birdlife', T)

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)

Joining, by = "name"

Use cross validation and dropping terms to find best model

full model: response ~ region_50km_ssm + region_50km_elevation_delta + biome_name + city_gdp_per_population + population_growth

Merlin data set

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + biome_name + city_gdp_per_population + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 19.47322

– CVE 19.47322 – Can we drop one?

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta + biome_name + city_gdp_per_population + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 19.7365

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + biome_name + city_gdp_per_population + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 19.68562

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + city_gdp_per_population + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 18.35732

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 19.39392

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + biome_name + city_gdp_per_population, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 19.12951

– drop biome_name to give smaller CVE of 18.35732 – can we drop another?

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta + city_gdp_per_population + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 18.49017

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + city_gdp_per_population + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 18.60964

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 18.26184

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + city_gdp_per_population, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 18.02666

– drop population_growth to give CVE of 18.02666 – can we drop another?

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta + city_gdp_per_population, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 18.15699

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + city_gdp_per_population, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 18.29845

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 17.9362

– drop city_gdp_per_population to give CVE of 17.9362 – can we drop another?

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 18.04985

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]

[1] 18.241

– best model with region_50km_ssm + region_50km_elevation_delta (CV error 17.9362)

summary(glm(data = merlin_city_data_fixed, formula = response ~ region_50km_ssm + region_50km_elevation_delta))

Call:
glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta, 
    data = merlin_city_data_fixed)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-7.6984  -2.8713  -0.5247   1.7119  16.9525  

Coefficients:
                              Estimate Std. Error t value Pr(>|t|)  
(Intercept)                  2.6583859  1.1311108   2.350   0.0202 *
region_50km_ssm             -0.1288796  0.0689039  -1.870   0.0636 .
region_50km_elevation_delta -0.0007078  0.0003457  -2.047   0.0426 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 17.38331)

    Null deviance: 2469.6  on 136  degrees of freedom
Residual deviance: 2329.4  on 134  degrees of freedom
AIC: 784.96

Number of Fisher Scoring iterations: 2

Birdlife data set

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + biome_name + city_gdp_per_population + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.755749

– can we drop a variable?

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta + biome_name + city_gdp_per_population + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.701032

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + biome_name + city_gdp_per_population + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.906615

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + city_gdp_per_population + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.455193

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.768164

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + biome_name + city_gdp_per_population, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.63928

– drop biome_name to give CVE of 6.455193 – can we drop another?

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta + city_gdp_per_population + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.515736

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + city_gdp_per_population + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.38495

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.417311

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + city_gdp_per_population, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.392071

– drop region_50km_elevation_delta to give CVE of 6.38495 – can we drop another?

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ city_gdp_per_population + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.476147

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.342025

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + city_gdp_per_population, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.331564

– drop population_growth to give CVE of 6.331564 – can we drop another?

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ city_gdp_per_population, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.414695

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.291299

– drop city_gdp_per_population to give CVE of 6.291299 – is this better than no variable?

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ 1, data = birdlife_city_data_fixed_no_boreal))$delta[1]

[1] 6.395701

– yes, just!

– so best model with birdlife is region_50km_ssm

summary(glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm))

Call:
glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_fixed)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.5353  -1.5461  -0.4124   1.3071  10.7572  

Coefficients:
                Estimate Std. Error t value Pr(>|t|)  
(Intercept)      1.26916    0.65041   1.951   0.0531 .
region_50km_ssm -0.08499    0.04115  -2.065   0.0408 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 6.214378)

    Null deviance: 865.45  on 136  degrees of freedom
Residual deviance: 838.94  on 135  degrees of freedom
AIC: 643.06

Number of Fisher Scoring iterations: 2

Lets look at SSM for both pools

ggplot(merlin_city_data_fixed_no_boreal, aes(x = region_50km_ssm, y = response)) + geom_point() + geom_smooth(method = "glm", se = F)

`geom_smooth()` using formula 'y ~ x'

ggplot(birdlife_city_data_fixed_no_boreal, aes(x = region_50km_ssm, y = response)) + geom_point() + geom_smooth(method = "glm", se = F)

`geom_smooth()` using formula 'y ~ x'

and include region_50km_elevation_delta for merlin

ggplot(merlin_city_data_fixed_no_boreal, aes(x = region_50km_ssm, y = response, size = region_50km_elevation_delta)) + geom_point() + geom_smooth(method = "glm", se = F)

`geom_smooth()` using formula 'y ~ x'

Check birdlife model fit

birdlife.fit <- glm(data = birdlife_city_data_fixed_no_boreal, formula = response ~ region_50km_ssm)
summary(birdlife.fit)

Call:
glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_fixed_no_boreal)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.5693  -1.5460  -0.4392   1.2913  10.7264  

Coefficients:
                Estimate Std. Error t value Pr(>|t|)  
(Intercept)      1.23286    0.65157   1.892   0.0606 .
region_50km_ssm -0.08135    0.04133  -1.969   0.0511 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 6.216274)

    Null deviance: 857.07  on 135  degrees of freedom
Residual deviance: 832.98  on 134  degrees of freedom
AIC: 638.43

Number of Fisher Scoring iterations: 2

with(summary(birdlife.fit), 1 - deviance/null.deviance)

[1] 0.02810766

plot(birdlife.fit)

ggplot(birdlife_city_data_fixed_no_boreal, aes(x = region_50km_ssm, y = response)) + 
  geom_point(size=1) + 
  geom_smooth(method = "glm", se = F) +
  geom_text(aes(label = name), data = birdlife_city_data_fixed_no_boreal[c(16, 53, 72),], size = 3, position = "dodge", vjust = "inward", hjust = "inward", color = "red", angle=-15) +
  geom_point(data = birdlife_city_data_fixed_no_boreal[c(16, 53, 72),], color = "red") +
  theme_bw() +
  ylab("City Random Effect Intercept") + xlab("Regional (50km) SSM") + labs(title = "Birdlife")

`geom_smooth()` using formula 'y ~ x'
Warning: Width not defined. Set with `position_dodge(width = ?)`

ggsave("city_effect_richness__output__birdlife.jpg")

Saving 7.29 x 4.51 in image
`geom_smooth()` using formula 'y ~ x'
Warning: Width not defined. Set with `position_dodge(width = ?)`

Check Merlin model fit

merlin.fit <- glm(data = merlin_city_data_fixed_no_boreal, formula = response ~ region_50km_ssm + region_50km_elevation_delta)
summary(merlin.fit)

Call:
glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta, 
    data = merlin_city_data_fixed_no_boreal)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-7.7040  -2.8410  -0.5643   1.7350  16.9652  

Coefficients:
                              Estimate Std. Error t value Pr(>|t|)  
(Intercept)                  2.6290037  1.1334734   2.319   0.0219 *
region_50km_ssm             -0.1238835  0.0693129  -1.787   0.0762 .
region_50km_elevation_delta -0.0007285  0.0003473  -2.097   0.0378 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 17.43624)

    Null deviance: 2458.9  on 135  degrees of freedom
Residual deviance: 2319.0  on 133  degrees of freedom
AIC: 779.68

Number of Fisher Scoring iterations: 2

with(summary(merlin.fit), 1 - deviance/null.deviance)

[1] 0.05688841

plot(merlin.fit)

ggplot(merlin_city_data_fixed_no_boreal, aes(x = region_50km_ssm, y = response)) + 
  geom_point(aes(size = region_50km_elevation_delta)) + 
  geom_smooth(method = "glm", se = F) +
  geom_text(aes(label = name), data = merlin_city_data_fixed_no_boreal[c(24, 30, 42),], size = 3, position = "dodge", vjust = "inward", hjust = "inward", color = "red", angle=-15) +
  geom_point(data = merlin_city_data_fixed_no_boreal[c(24, 30, 42),], color = "red") +
  theme_bw() +
  theme(legend.position="bottom") +
  ylab("City Random Effect Intercept") + xlab("Regional (50km) SSM") + labs(title = "eBird") + guides(size=guide_legend(title="Regional (50km) Elevation Delta"))

`geom_smooth()` using formula 'y ~ x'
Warning: Width not defined. Set with `position_dodge(width = ?)`

ggsave("city_effect_richness__output__merlin.jpg")

Saving 7.29 x 4.51 in image
`geom_smooth()` using formula 'y ~ x'
Warning: Width not defined. Set with `position_dodge(width = ?)`

How much variation have we explained?

merlin_city_data_fixed_no_boreal$residuals <- resid(merlin.fit)
ggplot(merlin_city_data_fixed_no_boreal, aes(y = response, x = residuals)) + 
  geom_smooth(method = "lm", se = F) +
  geom_point(aes(color = realm)) + 
  geom_text(aes(label = name), data = merlin_city_data_fixed_no_boreal[c(24, 30, 42),], size = 4, position = "dodge", vjust = "inward", hjust = "inward") + 
  labs(title = "Merlin", subtitle = paste("Correlation", cor(merlin_city_data_fixed_no_boreal$residuals, merlin_city_data_fixed_no_boreal$response))) +
  theme_bw()

`geom_smooth()` using formula 'y ~ x'
Warning: Width not defined. Set with `position_dodge(width = ?)`

ggplot(birdlife_city_data_fixed_no_boreal, aes(y = response, x = residuals)) + 
  geom_smooth(method = "lm", se = F, alpha = 0.5) +
  geom_point(aes(color = realm)) + 
  geom_text(aes(label = name), data = birdlife_city_data_fixed_no_boreal[c(16, 53, 72),], size = 4, position = "dodge", vjust = "inward", hjust = "inward") +
  labs(title = "Birdlife", subtitle = paste("Correlation", cor(birdlife_city_data_fixed_no_boreal$residuals, birdlife_city_data_fixed_no_boreal$response))) +
  theme_bw()

`geom_smooth()` using formula 'y ~ x'
Warning: Width not defined. Set with `position_dodge(width = ?)`

Check AIC